Design and Simulation of Two Stroke Engines

Design and Simulation of Two-Stroke Engines
temperature Tj = TQXJ (2.18.25)
particle velocity cs = G5a0(xp - Xq) (2.18.26)
2.18.5 Singularities during the interpolation procedure
It is obvious that arithmetic problems could arise with the procedure given in Sec. 2.18.4
if the values of XR and XRI, or the values of XL and XLI, are equal. This would certainly be
true in a model start-up situation, where the pipes would be "dead" and all of the array elements
of pressure amplitude ratio XR, XRI, XL and XLI would be unity. In that situation the
values of A and B would be zero, C and D would be infinity and the calculation would
collapse. Therefore, separate solutions are required for the wave pressures, Xp and Xq, in
these unique situations, either at start-up or as cover during the course of a complete calculation.
The solution is fairly straightforward using Eqs. 2.18.16 and 2.18.17, for the three possibilities
(a)-(c) involved.
In case (i) the following is the solution if it is true that XR is equal to XRI:
Hence,
Hence,
Xq =
X p = X R1
1 + D + G4Xj
In case (ii) the following is the solution if it is true that XL is equal to XLI:
X P =
x q = XLI
1 + C + G4XC
G* + 1
(2.18.27)
(2.18.28)
(2.18.29)
(2.18.30)
In case (iii) the following is the solution if it is true that XR is equal to XRI and also that
XL is equal to XLI :
and,
x q = X LI
Xp = XRI
150
(2.18.31)
(2.18.32)